Maths Book back answers and solution for Exercise questions - Solve the following system of linear equations by matrix inversion method:

**EXERCISE 1.3**

1. Solve the following system of linear equations by matrix
inversion method:

(i) 2*x** *+
5 *y *= -2, *x *+ 2 *y *= -3

(ii) 2*x *- *y *= 8, 3*x *+ 2 *y *= -2

(iii) 2*x *+ 3*y *- *z *= 9, *x *+ *y *+ *z *= 9, 3*x *- *y *- *z *= -1

(iv) *x *+ *y *+ *z *- 2 = 0, 6*x *- 4 *y *+ 5*z *- 31 = 0, 5*x *+ 2 *y *+ 2*z *= 13

2. If find the products AB and
BA and hence solve the system of equations *x *+ *y *+ 2*z *= 1, 3*x *+ 2 *y *+ *z *= 7, 2*x *+ *y *+ 3*z *= 2.

3. A man is appointed in a job with a monthly salary of
certain amount and a fixed amount of
annual increment. If his salary was â‚¹ 19,800 per month at the
end of the first month after 3 years of service
and â‚¹ 23,400 per month at the end of the first month after 9 years of service, find his starting salary and his annual increment. (Use matrix inversion
method to solve the
problem.)

4. Four men and 4 women
can finish a piece of work jointly
in 3 days while 2 men and 5 women can
finish the same work jointly
in 4 days. Find the time taken
by one man alone and that of one
woman alone to finish the same work by using matrix inversion
method.

5. The prices of three commodities *A*, *B *and *C *are â‚¹ *x*, *y *and *z *per units respectively. A person *P *purchases 4 units of *B *and
sells two units of *A *and 5 units of *C *. Person *Q *purchases 2 units of *C *and
sells 3 units of *A *and one unit of *B *. Person *R *purchases one unit of *A *and
sells 3 unit of *B *and one unit of *C *. In the process, *P*,*Q *and *R *earn â‚¹ 15,000, â‚¹ 1,000 and â‚¹ 4,000 respectively. Find the prices
per unit of *A*, *B *and *C *. (Use matrix
inversion method to solve the problem.)

**Answers for **Exercise 1.3**:**

1. (i) x = -11, y = 4

(ii) x = 2, y = -4

(iii) x = 2, y = 3, z = 4

(iv) x = 3, y = -2, z = 1

2. x = 2, y = 1, z = -1

3. â‚¹ 18000, â‚¹ 600

4. 18 days, 36 days

5. â‚¹ 2000, â‚¹ 1000, â‚¹ 3000

Tags : Problem Questions with Answer, Solution , 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Exercise 1.3: Matrices linear equations by matrix inversion method | Problem Questions with Answer, Solution

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